Article
Engineering, Marine
Mostafa M. A. Khater, Samir A. Salama
Summary: This article investigates novel soliton wave solutions of the nonlinear fractional ill-posed Boussinesq dynamic wave equation. The obtained solutions are explained in terms of their dynamic characteristics using the extended Riccati-expansion method, and their accuracy is verified by comparing them with semi-analytical solutions. The superiority of the extended Riccati-expansion method over the original method is discussed, and the solutions are further validated by submitting them back into the original model using Mathematica 12 software.
JOURNAL OF OCEAN ENGINEERING AND SCIENCE
(2022)
Article
Materials Science, Multidisciplinary
Asim Zafar, M. Raheel, Ali M. Mahnashi, Ahmet Bekir, Mohamed R. Ali, A. S. Hendy
Summary: This paper explores new soliton solutions of the truncated M-fractional (1+1)-dimensional non-linear Kaup-Boussinesq system using various techniques and discusses the analysis of long waves in shallow water and the effect of fractional order derivative.
RESULTS IN PHYSICS
(2023)
Article
Materials Science, Multidisciplinary
Shumaila Javeed, Mustafa Inc, Muhammad Awais Abbasi, K. H. Mahmoud, Zain Ul Abadin Zafar, Sohail Razzaq
Summary: This paper proposes an exponential function method (EFM) to solve the generalized Calogero-Bogoyavlenskii-Schiff equation, (3+1) dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov equation, and Variant Boussinesq equation. The solitary, cuspon, and periodic wave solutions are obtained and presented graphically. The soliton solutions of these equations play a typical role in expressing various wave transmissions in natural instances, particularly in shallow wave kinetics. The results suggest that EFM is an effective and useful technique for handling nonlinear engineering problems in oceans.
RESULTS IN PHYSICS
(2022)
Article
Mathematics, Applied
Lingfei Li, Yongsheng Yan, Yingying Xie
Summary: In this paper, a new extended (3 + 1)-dimensional generalized Kadomtsev-Petviashvili (KP)-Boussinesq equation is proposed and investigated. This equation models the transmission of tsunami waves at the bottom of the ocean and nonlinear ion-acoustic waves in magnetized dusty plasma. The obtained rational and semi-rational solutions are classified and analyzed.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Physics, Multidisciplinary
Yu Chen, Xing Lu, Xiao-Li Wang
Summary: This article focuses on the (3+1)-dimensional generalized breaking soliton (GBS) equation, which describes a Riemann wave propagating along three spatial dimensions. The Wronskian solutions are derived for the (3+1)-dimensional GBS equation based on the Plucker relation for determinants. The lump-soliton solutions are generated by virtue of the test function method. Through the Backlund transformation (BT), various solutions are obtained by specifically choosing different seed solutions, including the Wronskian solutions and the interaction solutions. The relation between the Wronskian solutions and interaction solutions is established based on BT. The study of the (3+1)-dimensional GBS equation provides theoretical guidance for solving equations and increases the diversity of exact solutions.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Materials Science, Multidisciplinary
Tukur A. Sulaiman, Abdullahi Yusuf, Fairouz Tchier, Mustafa Inc, F. M. O. Tawfiq, F. Bousbahi
Summary: In this work, the Lie-Backlund symmetry generators and corresponding conservation laws for the general Boussinesq equation are studied using a new conservation theorem and symmetry analysis method. Some important soliton solutions for the equation are constructed by means of two effective analytical schemes, and the physical features of these solutions are plotted to provide a clear outlook.
RESULTS IN PHYSICS
(2021)
Article
Mechanics
Yu Chen, Xing Lue
Summary: This article discusses the Wronskian solutions to the B-type Kadomtsev-Petviashvili (BKP) equation based on the Plucker relation. Rational solutions, positon solutions, negaton solutions, and complexiton solutions to the BKP equation are directly constructed. The Wronskian formulation is used to generate rational solutions in the form of determinants, and a polynomial identity is demonstrated to show that a linear combination of two Wronskian polynomial solutions of different orders is again a solution to the bilinear BKP equation.
Article
Mathematics, Interdisciplinary Applications
Hang Xu
Summary: A generalized homotopy-based approach is developed to provide highly accurate solutions for fractional differential equations. By introducing a scaling transformation, the computational domain of the nonlinear Riccati differential equations is reduced to [0,1]. The proposed method is shown to be effective and accurate through error analysis, making it a reliable analytical approach for solving strongly nonlinear problems in fractional calculus.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Materials Science, Multidisciplinary
Shao-Wen Yao, Md Nuruzzaman, Dipankar Kumar, Nishat Tamanna, Mustafa Inc
Summary: This study derives lump solutions for a new integrable (3 + 1)-dimensional Boussinesq equation and its dimensionally reduced equations using the Hirota bilinear method and Maple. The derived lump solutions display two trough positions and one crest position, with the amplitudes and shapes of the lump waves remaining constant during propagation but changing their positions. Graphical outputs of the propagations of the obtained lump wave solutions illustrate the changes in trough and crest positions over time with constant velocity, with the free parameters of the model playing a significant role in altering the shapes and amplitudes of the waves.
RESULTS IN PHYSICS
(2023)
Article
Physics, Applied
Jamil Abbas Haider, Noor Muhammad, Sohail Nadeem, Saleem Asghar
Summary: The Jacobi elliptic function expansion method is used to find periodic solutions of nonlinear equations, which is more extensive than expanding the hyperbolic tangent series and can produce periodic shock wave solutions such as solitary wave solutions.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2022)
Article
Mathematics, Applied
Yusuf Ucar, Alaattin Esen, Berat Karaagac
Summary: In this study, the Galerkin finite element method was applied to solve the good and bad Boussinesq equations, providing numerical solutions. The fourth order Runge-Kutta method was used to obtain numerical solutions, and error norms were used to test the accuracy of the solutions. The research investigated solitary wave motion, interaction of solitary waves, and blow-up solutions related to the interaction of two solitary waves.
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
(2021)
Article
Engineering, Civil
Allen June Buenavista, Chuan Wang, Yueqing Xie, Benjamin Gilfredder, Sven Frei, Pere Masque, Grzegorz Skrzypek, Shawan Dogramaci, James L. McCallum
Summary: Quantifying water flux between surface water and groundwater is crucial for water balance determination, surface water quality control, and sustainable allocation of water resources. By analyzing variations in 222Rn activity in sediments, water flow and residence times can be inferred. This study emphasizes the importance of accounting for upward flows in predicting groundwater exchange with surface water bodies.
JOURNAL OF HYDROLOGY
(2023)
Article
Engineering, Marine
Sachin Kumar, Setu Rani
Summary: This paper systematically investigates the exact solutions to an extended (2+1)-dimensional Boussinesq equation using the Lie symmetry analysis method. The vector fields, commutation relations, optimal systems, two stages of reductions, and exact solutions to the given equation are obtained with the help of the Lie group method. The behavior of the obtained results for multiple cases of symmetries is demonstrated through three-and two-dimensional dynamical wave profiles.
JOURNAL OF OCEAN ENGINEERING AND SCIENCE
(2022)
Article
Mathematics, Interdisciplinary Applications
Aref Sarhan, Aliaa Burqan, Rania Saadeh, Zeyad Al-Zhour
Summary: This paper presents the series solutions of the nonlinear time-fractional coupled Boussinesq-Burger equations using the Laplace-residual power series technique. An attractive numerical example is used to verify the efficiency and reliability of the proposed method. The obtained results demonstrate the compatibility and accuracy of this algorithm for fractional-order solutions in engineering and physical applications.
FRACTAL AND FRACTIONAL
(2022)
Article
Mechanics
W. P. Sun, K. L. Miao, Y. P. Yu, C. W. Lim
Summary: In this paper, a highly accurate analytical approximation solution method to a class of mixed-parity Duffing equation is proposed. The method first qualitatively analyzes the system and constructs an analytic approximate periodic solution within the parametric range. Higher precision approximate solutions are then obtained by combining Newton's method and harmonic balance method, showing excellent approximation accuracy compared to numerical solutions.
INTERNATIONAL JOURNAL OF APPLIED MECHANICS
(2021)